Question

Write the solution set for equation 7x - 2y = 8 with this replacement set: {(1,-1),(2,3), (0,-4), (4,10)}. List your answers from least to greatest based on the x value and without any spaces.

Answer 1

Any point in the cartesian coordinates actually has the structure:
\[A(x , f(x))\]
But, since it's unnecesarly complex to actually look at it like that, let's say that:
\[y=f(x)\]
therefore:
\[A(x,y)\]
So, moving on to the problem in question, we have the equation of:
\[7x-2y=8\]
Now, something very very important when we evaluate points i a given equality, and that is that in order for it to be a solution it has to satisfy the equation.
What do I mean?
By that I mean. that when I replace the point, it has to give me the constant that it it actually equal to. Lt's say for example, a very general equation:
\[Ax+By=C\]
And we say that point P(m,n) acutally is a solution for that equation, then the following must be true:
\[A(m)+B(n)=C\]
The only thing i did was replace the coordinates of the point in te equation, and for it to be a solution, the number it gives me must be equal to the C on the left side of the equality.
A, B, C, m, n are any real number you like.

So, let's return:
\[7x-2y=8\]
let's take one of the numbers we are given and replace it there, say (1,-1).
Now, I already told you, that any point has the structure of A(x,y), so by simply looking you can see that x=1 and y=-1.
So, let's take the equation 7x-2y=8 and instead of x and y let's put 1 and -1 .
It'll look like this:
\[7(1)-2(-1)=8\]
\[7+2=8\]
\[9 \neq 8\]
Since 9 is not equal to 8, (1,-1) is not a solution for the equality.